Question: Solve for $x$ and $y$ using elimination. ${4x+y = 27}$ ${3x+2y = 24}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-2$ ${-8x-2y = -54}$ $3x+2y = 24$ Add the top and bottom equations together. $-5x = -30$ $\dfrac{-5x}{{-5}} = \dfrac{-30}{{-5}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {4x+y = 27}\thinspace$ to find $y$ ${4}{(6)}{ + y = 27}$ $24+y = 27$ $24{-24} + y = 27{-24}$ ${y = 3}$ You can also plug ${x = 6}$ into $\thinspace {3x+2y = 24}\thinspace$ and get the same answer for $y$ : ${3}{(6)}{ + 2y = 24}$ ${y = 3}$